Template:Number-theoretic algorithms

v t e Number-theoretic algorithms
Primality tests	AKS test APR test Baillie–PSW ECPP test Elliptic curve Pocklington Fermat Lucas Lucas–Lehmer Lucas–Lehmer–Riesel Proth's theorem Pépin's Solovay–Strassen Miller–Rabin Trial division
Prime-generating	Sieve of Atkin Sieve of Eratosthenes Sieve of Sundaram Wheel factorization
Integer factorization	CFRAC Dixon's ECM Euler's Pollard's rho p − 1 p + 1 QS GNFS SNFS Rational sieve Fermat's Shanks' square forms Trial division Shor's
Multiplication	Ancient Egyptian Karatsuba Toom–Cook Schönhage–Strassen Fürer's
Discrete logarithm	Baby-step giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve
GCD	Binary GCD Euclidean Extended Euclidean Lehmer's
Modular square root	Cipolla Pocklington's Tonelli–Shanks
Other algorithms	Chakravala Cornacchia Integer relation Integer square root Modular exponentiation Schoof's
Italics indicate that algorithm is for numbers of special forms Smallcaps indicate a deterministic algorithm